Paper: arXiv 2510.21156

Authors: Dong Yan, Ke Zhou, Zirun Wang, Xin-Jiang He

Abstract

In this paper, we investigate a portfolio selection problem with transaction costs under a two-factor stochastic volatility structure, where volatility follows a mean-reverting process with a stochastic mean-reversion level. The model incorporates both proportional exogenous transaction costs and endogenous costs modeled by a stochastic liquidity risk process. Using an option-implied approach, we extract an S-shaped utility function that reflects investor behavior and apply its concave envelope transformation to handle the non-concavity. The resulting problem reduces to solving a five-dimensional nonlinear Hamilton-Jacobi-Bellman equation. We employ a deep learning-based policy iteration scheme to numerically compute the value function and the optimal policy. Numerical experiments are conducted to analyze how both types of transaction costs and stochastic volatility affect optimal investment decisions.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a sophisticated continuous-time framework combining two-factor stochastic volatility, dual transaction costs, option-implied S-shaped utility, and a high-dimensional nonlinear HJB equation solved via deep learning. While it features strong theoretical rigor and option-based calibration, empirical validation relies largely on numerical simulations rather than extensive out-of-sample trading backtests.

Research Flowchart

  flowchart TD
    A[Research Goal: Portfolio Selection under Stochastic Volatility & Transaction Costs] --> B[Model Formulation & Inputs]
    
    B -->|2-Factor Stochastic Volatility<br>S-Shaped Utility & Concave Envelope<br>Exogenous & Endogenous Liquidity Costs| C[5D Nonlinear HJB Equation]
    
    C --> D[Deep Learning-Based Policy Iteration Scheme]
    
    D --> E[Numerical Experiments & Sensitivity Analysis]
    
    E --> F[Key Outcomes: Optimal Policy Execution & Insights on Cost/Volatility Impact]

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1 of 61 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.